Teaching Mathematics in Colleges and Universities C: Case Studies for Today's Classroom Faculty Edition

by Friedberg, Solomon

• ISBN13: 9780821828755
• ISBN10: 0821828754
• Format: Paperback
• Copyright: 2001-06-01
• Publisher: Amer Mathematical Society

Summary

Progress in mathematics frequently occurs first by studying particular examples and then by generalizing the patterns that have been observed into far-reaching theorems. Similarly, in teaching mathematics one often employs examples to motivate a general principle or to illustrate its use. This volume uses the same idea in the context of learning how to teach: By analyzing particular teaching situations, one can develop broadly applicable teaching skills useful for the professional mathematician. These teaching situations are the Case Studies of the title. Just as a good mathematician seeks both to understand the details of a particular problem and to put it in a broader context, the examples presented here are chosen to offer a serious set of detailed teaching issues and to afford analysis from a broad perspective. Each case raises a variety of pedagogical and communication issues that may be explored either individually or in a group facilitated by a faculty member. Teaching notes for such a facilitator are included for each Case in the Faculty Edition. The methodology of Case Studies is widely used in areas such as business and law. The consideration of the mathematics cases presented here will help readers to develop teaching skills for their own classrooms.

Table of Contents

Introduction

Fourteen case studies: Changing sections Emily's test Fundamental problems

part I Making the Grade (College algebra version/Calculus I version/Multivariable calculus version) Making waves Order out of chaos Pairing up

The quicksand of problem four Salad days Seeking points

Study habits Studying the exam (College algebra questions/Calculus II questions/Multivariable calculus questions)

There's something about Ted part I What were they thinking?

Supporting materials for faculty: Developing effective mathematics teaching assistants using case studies: An introduction for faculty Using case studies in aTA-development program

Types of cases Summaries of cases How these cases were created Changing sections, teaching guide

Emily's test, teaching guide Fundamental problems part II (Fundamental problems, teaching guide)

Making the grade, teaching guide Making waves part II (Making waves, teaching guide)

Order out of chaos, teaching guide Pairing up, teaching guide

The quicksand of problem four, teaching guide Salad days, teaching guide Seeking points, teaching guide Study habits, teaching guide Studying the exam, teaching guide (College algebra version/Calculus II version/Multivariable calculus version)

There's something about Ted Part II/There's something about Ted, teaching guide

What were they thinking?, teaching guide

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